Displaying similar documents to “Finite subschemes of abelian varieties and the Schottky problem”

The small Schottky-Jung locus in positive characteristics different from two

Fabrizio Andreatta (2003)

Annales de l’institut Fourier

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We prove that the locus of Jacobians is an irreducible component of the small Schottky locus in any characteristic different from 2 . The proof follows an idea of B. van Geemen in characteristic 0 and relies on a detailed analysis at the boundary of the q - expansion of the Schottky-Jung relations. We obtain algebraically such relations using Mumford’s theory of 2 -adic theta functions. We show how the uniformization theory of semiabelian schemes, as developed by D. Mumford, C.-L. Chai...

Maximal compatible splitting and diagonals of Kempf varieties

Niels Lauritzen, Jesper Funch Thomsen (2011)

Annales de l’institut Fourier

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Lakshmibai, Mehta and Parameswaran (LMP) introduced the notion of maximal multiplicity vanishing in Frobenius splitting. In this paper we define the algebraic analogue of this concept and construct a Frobenius splitting vanishing with maximal multiplicity on the diagonal of the full flag variety. Our splitting induces a diagonal Frobenius splitting of maximal multiplicity for a special class of smooth Schubert varieties first considered by Kempf. Consequences are Frobenius splitting...

The Frobenius action on rank 2 vector bundles over curves in small genus and small characteristic

Laurent Ducrohet (2009)

Annales de l’institut Fourier

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Let X be a general proper and smooth curve of genus 2 (resp. of genus 3 ) defined over an algebraically closed field of characteristic p . When 3 p 7 , the action of Frobenius on rank 2 semi-stable vector bundles with trivial determinant is completely determined by its restrictions to the 30 lines (resp. the 126 Kummer surfaces) that are invariant under the action of some order 2 line bundle over X . Those lines (resp. those Kummer surfaces) are closely related to the elliptic curves (resp....

Geometry of the genus 9 Fano 4-folds

Frédéric Han (2010)

Annales de l’institut Fourier

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We study the geometry of a general Fano variety of dimension four, genus nine, and Picard number one. We compute its Chow ring and give an explicit description of its variety of lines. We apply these results to study the geometry of non quadratically normal varieties of dimension three in a five dimensional projective space.

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

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We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of N is glicci, that is, whether every zero-scheme in 3 is glicci. We show that a general set of n 56 points in 3 admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in 3 .